g-index
{{Short description|Citation metric}}
{{DISPLAYTITLE:g-index}}
{{Citation metrics}}
{{For|the G-index in photometry|Spectral G-index}}
The g-index is an author-level metric suggested in 2006 by Leo Egghe.{{cite journal
|last1=Egghe |first1=Leo
|year=2006
|title=Theory and practise of the g-index
|journal=Scientometrics
|volume=69 |issue=1 |pages=131–152
|doi=10.1007/s11192-006-0144-7
|hdl=1942/981
|s2cid=207236267
|hdl-access=free
}} The index is calculated based on the distribution of citations received by a given researcher's publications, such that given a set of articles ranked in decreasing order of the number of citations that they received, the g-index is the unique largest number such that the top g articles received together at least g2 citations. Hence, a g-index of 10 indicates that the top 10 publications of an author have been cited at least 100 times (102), a g-index of 20 indicates that the top 20 publications of an author have been cited 400 times (202).
It can be equivalently defined as the largest number n of highly cited articles for which the average number of citations is at least n. This is in fact a rewriting of the definition
:
as
:
The g-index is an alternative for the older h-index. The h-index does not average the number of citations. Instead, the h-index only requires a minimum of n citations for the least-cited article in the set and thus ignores the citation count of very highly cited publications. Roughly, the effect is that h is the number of works of a quality threshold that rises as h rises; g allows citations from higher-cited works to be used to bolster lower-cited works in meeting this threshold. In effect, the g-index is the maximum reachable value of the h-index if a fixed number of citations can be distributed freely over a fixed number of publications. Therefore, in all cases g is at least h, and is in most cases higher. The g-index often separates authors based on citations to a greater extent compared to the h-index. However, unlike the h-index, the g-index saturates whenever the average number of citations for all publications exceeds the total number of publications; the way it is defined, the g-index is not adapted to this situation. However, if an author with a saturated g-index publishes more, their g-index will increase.
| class="wikitable"
|+ An example of two authors who both have 10 publications, both authors have a h-index of 6. However, Author 1 has a g-index of 10, while Author 2 has a g-index of 7. ! ! Author 1 ! Author 2 |
| Work 1
| 30 | 10 |
| Work 2
| 17 | 9 |
| Work 3
| 15 | 9 |
| Work 4
| 13 | 9 |
| Work 5
| 8 | 8 |
| Work 6
| 6 | 6 |
| Work 7
| 5 | 5 |
| Work 8
| 4 | 4 |
| Work 9
| 3 | 2 |
| Work 10
| 1 | 1 |
| Total cites
| 102 | 63 |
| Average cites
| 10,2 | 6,3 |
The g-index has been characterized in terms of three natural axioms by Woeginger (2008).
{{cite journal
|last1=Woeginger |first1=Gerhard J. |author-link=Gerhard J. Woeginger
|year=2008
|title=An axiomatic analysis of Egghe's g-index
|journal=Journal of Informetrics
|volume=2 |issue=4 |pages=364–368
|doi=10.1016/j.joi.2008.05.002
}} The simplest of these three axioms states that by moving citations from weaker articles to stronger articles, one's research index should not decrease. Like the h-index, the g-index is a natural number and thus lacks in discriminatory power. Therefore, Tol (2008) proposed a rational generalisation.
{{cite journal
|last1=Tol |first1=Richard S. J.
|year=2008
|title=A rational, successive g-index applied to economics departments in Ireland
|journal=Journal of Informetrics
|volume=2 |issue=2 |pages=149–155
|doi=10.1016/j.joi.2008.01.001
}} [http://ideas.repec.org/p/sgc/wpaper/147.html Preprint].{{Clarify|reason=What rational generalization did he propose?|date=April 2010}}
Tol also proposed a collective g-index.
: Given a set of researchers ranked in decreasing order of their g-index, the g1-index is the (unique) largest number such that the top g1 researchers have on average at least a g-index of g1.